Finite Group DatabasebetaFinite Group DatabasebetaOrder 16448.
294 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D257 |
| commutator, socle, cosocle | C22×C257 | C24 |
| Fitting | C2×#41×C257 | C2 |
| hypercenter | C2×#41 | D257 |
| hypocenter | C257 | #537 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16861618 | C2 | semidirect |
| 2. #22551571 | C2 | semidirect |
| 3. #22551568 | C2 | semidirect |
| 4. #22551566 | C2 | semidirect |
| 5. #22551564 | C2 | semidirect |
| 6. #22551563 | C2 | semidirect |
| 7. C2×C4⋊Dic257 | C2 | semidirect |
| 8. C2×#41×C257 | C2 | semidirect |
| 42. C2×C4×C257 | D4 | semidirect |
| 67. C257 | #537 | semidirect |
| 70. C2×#41 | D257 | semidirect |
| 110. C2×C4 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861618 | 2 |
| #22551571 | 2 |
| #22551568 | 2 |
| #22551566 | 2 |
| #22551564 | 2 |
| #22551563 | 2 |
| C2×C4⋊Dic257 | 2 |
| C2×#41×C257 | 2 |
| #537 | 257 |